> The student’s home is located at the coordinates (1, 1), and the university is at the coordinates (N, M).
It means, for example, if N == 1 && M == 1 then university have same coordinates as home. Of course we can not use any roads in such case. But according to the sentence:
> There are a total of N streets running from north to south and M streets running from west to east.
there are some roads that can not be used. I think there should be N - 1 streets running from north to south and M - 1 streets running from west to east.